Question

find the measure of an interior angle of a regular hexagon (6 - sided polygon). hint: sum=(n - 2)180

Explanation:

Step1: Find sum of interior angles

For a polygon with $n$ sides, the sum of interior - angles formula is $S=(n - 2)\times180^{\circ}$. Here, $n = 6$ (hexagon), so $S=(6 - 2)\times180^{\circ}=4\times180^{\circ}=720^{\circ}$.

Step2: Calculate measure of one interior angle

Since a regular hexagon has all interior angles equal, if we let the measure of one interior angle be $x$, and there are $n = 6$ angles, then $x=\frac{S}{n}$. Substituting $S = 720^{\circ}$ and $n = 6$, we get $x=\frac{720^{\circ}}{6}=120^{\circ}$.

Answer:

$120$